Adhesion and electronic structure of graphene on hexagonal boron nitride substrates

We investigate the adsorption of graphene sheets on h-BN substrates by means of first-principles calculations in the framework of adiabatic connection fluctuation-dissipation theory in the random phase approximation. We obtain adhesion energies for different crystallographic stacking configurations and show that the interlayer bonding is due to long-range van der Waals forces. The interplay of elastic and adhesion energies is shown to lead to stacking disorder and moir\'e structures. Band structure calculations reveal substrate induced mass terms in graphene which change their sign with the stacking configuration. The dispersion, absolute band gaps and the real space shape of the low energy electronic states in the moir\'e structures are discussed. We find that the absolute band gaps in the moir\'e structures are at least an order of magnitude smaller than the maximum local values of the mass term. Our results are in agreement with recent STM experiments.Comment: 8 pages, 8 figures, revised and extended version, to appear in Phys. Rev.

HST/FOS spectra of PG 1351+64: An intrinsic absorber at low redshift

A 1 A resolution spectra of the nearby (z = 0.08797) Seyfert galaxy PG 1351+64 taken with the Faint Object Spectrograph (FOS) onboard the Hubble Space Telescope is presented. Spectral coverage runs from 1200-3200 A in the observed frame and includes emission and absorption features due to Ly-alpha, N 5, Si 4, C 4, and Mg 2. Three distinct intrinsic absorption systems in Ly-alpha, N 5, Si 4, and C 4, and tentatively in Mg 2, at velocities of 900 km/s, 1630 km/s, and 2900 km/s (plus or minus 100 km/s) relative to the emission-line redshift of the QSO were detected. The maximum relative velocity of these absorbers is less than 5000 km/s and therefore does not meet Weymann, Carswell, & Smith's criteria for Broad-Absorption-Line (BAL) QSO's at high-z. However, the absorptions are almost certainly intrinsic to the QSO given the low redshift of this object. In addition, PG 1351+64 is marginally radio-quiet, as are all BALQSO's, based on recent estimates of the radio-loud/radio-quiet dividing line. The narrow velocity width, less than 500 km/s, and low outflow velocities of the absorption systems are more similar to so called 'associated absorbers' seen at high-z in radio-loud quasars, but whose absorptions are thought to arise in clouds much farther from the nucleus (greater than 1 kpc) than are BAL clouds (1-10 pc). Despite the qualitative resemblance to the associated absorbers, the absorption systems in PG 1351+64 appear to be the low-luminosity analogs of BALQSO absorption troughs. The lower observed outflow velocities in PG 1351+64 are due to the much lower luminosity of the nuclear source in comparison to the high-z, high-luminosity BALQSO's. In addition, 'satellite' emission lines displaced 4000-5000 km/s blueward and redward of the Mg 2 emission were discovered

Coordinate time and proper time in the GPS

The Global Positioning System (GPS) provides an excellent educational example as to how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see \cite{ashby}) uses the Schwarzschild spacetime to deduce the {\it approximate} formula, ds/dt\approx 1+V-\frac{|\vv|^2}{2}, for the relation between the proper time rate $s$ of a satellite clock and the coordinate time rate $t$. Here $V$ is the gravitational potential at the position of the satellite and \vv is its velocity (with light-speed being normalized as $c=1$). In this note we give a different derivation of this formula, {\it without using approximations}, to arrive at ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}, where \n is the normal vector pointing outward from the center of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to ds/dt=\sqrt{1+2V-|\vv|^2}. We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.Comment: 5 pages, revised, over-over-simplified... Does anyone care that the GPS uses an approximate formula, while a precise one is available in just a few lines??? Physicists don'

Quantum Mechanics of Extended Objects

We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, namely, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example, we theoretically predict the phenomenological coupling constant of the $\omega$ meson, which mediates the short range and repulsive nucleon force, as well as the repulsive core radius.Comment: RevTex, 24 pages, 1 eps and 5 ps figures, format change

A simulation of the Schwinger model in the overlap formalism

In the continuum, the single flavor massless Schwinger model has an exact global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a nonzero expectation value for the bilinear $\bar\psi\psi$. We show that a lattice formulation of this model, using the overlap formalism to treat the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo simulation of the complete system yields the correct value of the fermion condensate and shows unambiguously that it originates from the sector of topological charge equal to unity.Comment: Plain TeX file, 9 pages

Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing

We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her with the previously found constraints, these form a sufficient number of second class constraints so that the phase space is reduced to one pair of canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to both the Bondi-Sachs and the Newman-Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behavior require the connection to fall off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off more slowly leads to logarithmic behavior which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum, and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.Comment: magnification set; pagination improved; 20 pages, plain te

Gravitational Waves from a Fissioning White Hole

We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.Comment: 11 pages, 6 figures, RevTeX

Gauge Theories in a Bag

We investigate multi-flavour gauge theories confined in d\es 2n-dimensional Euclidean bags. The boundary conditions for the 'quarks' break the axial flavour symmetry and depend on a parameter $\theta$. We determine the $\theta$-dependence of the fermionic correlators and determinants and find that a $CP$-breaking $\theta$-term is generated dynamically. As an application we calculate the chiral condensate in multi-flavour $QED_2$ and the abelian projection of $QCD_2$. In the second model a condensate is generated in the limit where the number of colours, $N_c$, tends to infinity. We prove that the condensate in $QCD_2$ decreases with increasing bag radius $R$ at least as $\sim R^{-1/N_cN_f}$. Finally we determine the correlators of mesonic currents in $QCD_2$.Comment: 40 pages, LATEX-fil